Dr. Leigh's work is dedicated to understanding a number of classical and current problems in physics and astrophysics, including:

• The classical gravitational three- and four-body problems. These problems extend all the back to Newton, with a rich and interesting history extending up to the present, since to this day they remain unsolved.
• Black holes of any mass (stellar-, intermediate- and super-massive) and the formation, evolution and final fate of binary stars containing black holes in dense stellar systems (i.e., open, globular and nuclear star clusters).
• The "initial conditions" problem for all types of star clusters and stellar systems. Simulations of stellar systems always begin with a well-defined set of initial conditions, but they are typically poorly constrained both observationally and theoretically. This is critical since what you get out of the simulations depends sensitively on what you put in.
• Understanding chaos in gravitational dynamics, to help mitigate our currently heavy reliance on computer simulations that remain in many ways very limited. This is arguably a problem that is unlikely to get much better in the near future, given the relatively recent death of Moore's Law.

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